leveque_dg.cc

The Leveque benchmark by discontinuous Galerkin method

#include "rheolef.h"
using namespace rheolef;
using namespace std;
#include "leveque.h"
#include "bdf.icc"
int main(int argc, char**argv) {
environment rheolef (argc, argv);
geo omega (argv[1]);
space Xh (omega, argv[2]);
size_t n_max = (argc > 3) ? atoi(argv[3]) : 1000;
size_t strip = (argc > 4) ? string(argv[4]) == "true" : false;
size_t p = (argc > 5) ? atoi(argv[5]) : min(Xh.degree()+1,bdf::pmax);
size_t d = omega.dimension();
Float tf = u::period(), delta_t = tf/n_max;
trial phi (Xh); test xi (Xh);
branch event ("t","phi");
vector<field> phi_h (p+1);
phi_h[0] = phi_h[1] = interpolate (Xh, phi0(d));
dout << event (0, phi_h[0]);
for (size_t n = 1; n <= n_max; n++) {
Float t = n*delta_t;
if (n % 10 == 0) derr << "[" << n << "]";
size_t pn = min(n,p);
form an = integrate ((bdf::alpha[pn][0]/delta_t*phi + dot(u(d,t),grad_h(phi)))*xi)
+ integrate ("internal_sides",
- dot(u(d,t),normal())*jump(phi)*average(xi)
+ 0.5*abs(dot(u(d,t),normal()))*jump(phi)*jump(xi));
field rhs(Xh, 0);
for (size_t i = 1; i <= pn; i++)
rhs += (bdf::alpha[pn][i]/delta_t)*phi_h[i];
field lh = integrate(rhs*xi);
problem pb (an);
pb.solve (lh, phi_h[0]);
check_macro (phi_h[0].max_abs() < 100, "BDF failed -- HINT: decrease delta_t");
if (!strip || n == n_max) dout << event (t, phi_h[0]);
for (size_t i = min(p,pn+1); i >= 1; i--)
phi_h[i] = phi_h[i-1];
}
derr << endl;
}
bdf.icc
BDF(p) backward differentiation formula – coefficients.
lh
field lh(Float epsilon, Float t, const test &v)
Definition: burgers_diffusion_operators.icc:25
phi
Float phi(const point &nu, Float a, Float b)
Definition: burgers_flux_godunov.icc:25
Float
see the Float page for the full documentation
branch
see the branch page for the full documentation
field
see the field page for the full documentation
form
see the form page for the full documentation
geo
see the geo page for the full documentation
problem
see the problem page for the full documentation
rheolef::dout
odiststream dout(cout)
see the diststream page for the full documentation
Definition: diststream.h:430
rheolef::derr
odiststream derr(cerr)
see the diststream page for the full documentation
Definition: diststream.h:436
space
see the space page for the full documentation
test
see the test page for the full documentation
trial
see the test page for the full documentation
leveque.h
The Leveque benchmark – function definition.
main
int main(int argc, char **argv)
Definition: leveque_dg.cc:30
bdf::alpha
Float alpha[pmax+1][pmax+1]
Definition: bdf.icc:28
bdf::pmax
constexpr size_t pmax
Definition: bdf.icc:26
mkgeo_ball.d
int d
Definition: mkgeo_ball.sh:154
mkgeo_ball.n
int n
Definition: mkgeo_ball.sh:150
rheolef::details::max_abs
T max_abs(const T &x)
Definition: keller_details.h:47
rheolef
This file is part of Rheolef.
Definition: compiler_eigen.h:37
rheolef::dot
rheolef::std enable_if ::type dot const Expr1 expr1, const Expr2 expr2 dot(const Expr1 &expr1, const Expr2 &expr2)
dot(x,y): see the expression page for the full documentation
Definition: vec_expr_v2.h:415
rheolef::grad_h
std::enable_if< details::is_field_convertible< Expr >::value,details::field_expr_v2_nonlinear_terminal_field< typename Expr::scalar_type,typename Expr::memory_type,details::differentiate_option::gradient >>::type grad_h(const Expr &expr)
grad_h(uh): see the expression page for the full documentation
Definition: field_expr_terminal.h:949
rheolef::integrate
std::enable_if< details::is_field_expr_v2_nonlinear_arg< Expr >::value &&! is_undeterminated< Result >::value, Result >::type integrate(const geo_basic< T, M > &omega, const Expr &expr, const integrate_option &iopt, Result dummy=Result())
see the integrate page for the full documentation
Definition: integrate.h:202
rheolef::interpolate
field_basic< T, M > interpolate(const space_basic< T, M > &V2h, const field_basic< T, M > &u1h)
see the interpolate page for the full documentation
Definition: interpolate.cc:233
rheolef::normal
details::field_expr_v2_nonlinear_terminal_function< details::normal_pseudo_function< Float > > normal()
normal: see the expression page for the full documentation
Definition: field_expr_terminal.h:439
rheolef.h
rheolef - reference manual
p
Definition: sphere.icc:25
phi0
Definition: leveque.h:37
phi
Definition: phi.h:25
u::period
static Float period()
Definition: leveque.h:32
u
Float u(const point &x)
Definition: transmission_error.cc:26